Formulating Equations for Warp Knitted Structures (Fabrics) Notations Design Area

Published by : International Journal of Engineering Research & Technology (IJERT) http://www.ijert.org ISSN: 2278-0181 Vol. 5 Issue 03, March-2016 Formulating Equations for Warp Knitted Structures (Fabrics) Notations Design Area

Dereje Berihun Sitotaw Textile Engineering Ethiopian institute of Textile and Fashion Technology, Bahir Dar University, Bahir Dar, Ethiopia

Abstract— this formula is developed to solve the problems In warp knitting the fabric is produced by the developments of repeated mistakes during the notations of warp knitted of lap instead of loop in weft knitting for it is formed by structures. Notation of warp knitted fabrics is not easy lapping movement of warp yarn guide. The lappings are two like that of weft knitted fabrics. The degree of shifting, types depending of the movement of guide bar with yarn design areas, numbers of overlaps are the main things relative to needle surface and termed as overlap and considered during warp knitted fabrics designing. The underlap. Overlap is the lateral movement of the guide bars formula was developed by considering degree of wale on the beard or hook side of the needle. This movement is shift and number of overlaps in one line in the knitted normally restricted to one needle space. Underlap is the fabrics/structure. The formula will help warp knit lateral movement of the guide bars on the side of the needle designers particularly for those designing without remote from the hook or beard. This movement is limited software. The formulation was done by analyzing only by the mechanical considerations. It is the connection different types of warp knit structures. between stitches in consecutive courses in a warp knitted fabric. The length of under lap is determined by the degree of Keywords—Warp knit, design area, pattern height, pattern width, wale shifts in warp knit structure. formulating equation, warp knit notations 2. WARP KNIT STRUCTURE NOTATIONS 1. INTRODUCTION Notations are symbolical representation of objects, structures, Warp knitting is a method of making a fabric by normal designs and fabrics. Warp knitted fabrics notation is an knitting means, in which the loops made from each warp are important part of fabric manufacturing. Notations of warp formed substantially along the length of the fabric. It is knitted fabrics are graphical representation of the designs characterized by the fact that each warp thread is fed more or using dot notations and elements of notations. Elements of k2less in line with the direction in which the fabric is warp knitted structure notations include mainly degree of produced. Each needle within the knitting width must be fed wale shift, number of overlaps in one line, numerical record with at least one separate and individual thread at each graph, sides of under laps and design area representation. course. It is the fastest method of converting yarn into fabric, These elements collaborate all together for full symbolical when compared with weaving and weft knitting representation of warp knitted structures/fabrics. Degrees of wale shift, number of overlap in one line and design area are the determining elements for the others. Many teachers, students, designers, warp knit technologists faced the problems of putting dots repeatedly by trial and error system for denoting warp knitted structures/fabrics. Problems of repeated erasing/adding dots arise mainly from the warp knitted structure/fabric notation element called design area. In these paper, formula for design area representation of warp knitted structures/fabrics is formulated to solve the notation problem for those who denote warp knitted structures using paper, pencil, pen, markers especially for those listed above.

2.1. Steps of warp knitted fabrics notation • Prepare rows and columns of dots that represent overlaps/needles • Use points to designate the needles of one bed, and crosses-the needles of the other bed (for two-bed machines). Figure 1: Tricot warp knitted fabric with wale shift 1 and course shift 1 design area 1x1 • Write the rows number on the left side (courses) from bottom to top as it is on the structure

IJERTV5IS030629 378 (This work is licensed under a Creative Commons Attribution 4.0 International License.) Published by : International Journal of Engineering Research & Technology (IJERT) http://www.ijert.org ISSN: 2278-0181 Vol. 5 Issue 03, March-2016

• Give numbers to the empty spaces between two type of machines these structures are produced from, and consecutive needles from right to left whole numbers for notation of each identified structures are done. single bed even number for double bed • Draw the path of a yarn in a design area only. Use 5. FORMULATING EQUATION FOR WARP closed loop for closed loops and open loop for open loops KNITTED STRUCTURE DESIGN AREA Using the main elements of warp knitted structures notation 3. TERMINOLOGIES RELATED TO ELEMENTS element such as degree of shifting and number of overlaps in OF DESIGN ELEMENTS AND THEIR SYMBOLIC one direction the formula can be developed easily. Let W REPRESENTATION represents the number of wales shift between consecutive overlaps, N represents number of overlaps in one direction, 3.1. Degree of shifting and Dw represents pattern width and Dh for pattern height. It is represented by Wx1. In which W is the number of wales Design area is the product of pattern height and pattern shifted to form second loop/between two consecutive width. Let we find pattern width and pattern height overlaps and 1 is the number of courses shifted is one. In separately. warp knitted structures wales can be shifted for designing purpose but courses are constant i.e. 1. 5.1. Pattern height Pattern height is determined by number of overlaps in one 3.2. Number of overlaps in one direction direction. As the number of overlap increases pattern height The number of needles a single warp is being knitted on and increases and reduced when number of overlap reduces. So, represented by N. For basic tricot structures the number of Dh = 2N-2 overlaps in one direction is always two whereas for basic = 2(N-1) ------(1), where N is the number of atlas there should be minimum of three. overlaps in one direction, 2 is the full movement of thread direction in the whole pattern (to the right then back to the 3.3. Sides of under laps left) and 1 is the course shift. The under laps (the ingoing and outgoing under laps) of a given overlap can be single sided or double sided relative to 5.2. Pattern width wale lines. Loops in a given side of a fabric can therefore be Pattern width depends on degree of shifting and number of single sided, double sided or combination of the two and overlaps in one direction. Both number of overlaps and determines the inclination of the overlaps. degree of wale shifting affects the pattern width of warp knitted structures notations. 3.4. Numerical record graph Dw = (WxN) – W + 1 It is the representation of warp knitted yarn movement in = W x (N-1) + 1------(2) overlapping, under lapping or both relative to needles. In a Where Dw is pattern width, W is degree of wale shift and N dot paper representation yarn parts lying on the needle (o) is the number of overlaps in one directions. and under the needle (u) has to be shown. This can be two stages or three stages. When names are given for the yarn 5.3. Pattern Area laying on the needles (o) two stages is used and when names Pattern area is determined by multiplying pattern width and given to yarn both laying on the needles and under the needle pattern height but it does not mean that pattern area has three stages numerical record graph is used. Assign two constant value rather it has two values those managed numbers for 2 stage and three numbers for 3 stage and start separately. from bottom end of yarn and go towards up (i.e. in the DwxDh = multiplication of equation 2 and equation 1. knitting direction). = (Wx (N-1) + 1) x (2(N-1)) ------(3). With this formula we can determine the optimum number of 3.5. Design Area representation dots for the different type of warp knitted structures It is represented by DwxDh. This represents the area in which notations. The design area is measured in number of dots in the number of courses and wales are put in the paper for the vertical (courses) and horizontal (wales). denoting the repeat of the fabric/structure. It has two main parts termed as pattern height and pattern width. Pattern 5.4. Advantages of the formula height is number of courses where pattern looping over on a yarn path whereas Pattern width is number of wales where Before this formula we were face many problems in the the single thread passes. The design area determines the other notation of basic warp knit structures for those produced on elements of warp knitted fabric notation. single bed and double bed warp knitting machines with different number of degree of shifting and number of overlaps in one line using crochet, tricot and raschel warp 4. MATERIALS AND METHODS knitting machines. With this formula related problems like Different warp knitted structures are analyzed and identified repeated erasing and putting of dots are solved. using magnifying glass, Tape meter, cutting dies, Paper, Other notation parameters of warp knit structures such as pencil and pen. Tricot, crochet, atlas with their derivatives is sides of underlap and numerical record graph are easily analyzed for using it as an input in determining the design determined from the design area. area and other notation parameters. The formulation was With this formula designing of warp knitted structures are begin with structural analysis, then grouping according to the more economical in that it saves both time and money by

IJERTV5IS030629 379 (This work is licensed under a Creative Commons Attribution 4.0 International License.) Published by : International Journal of Engineering Research & Technology (IJERT) http://www.ijert.org ISSN: 2278-0181 Vol. 5 Issue 03, March-2016 providing accurate number of dots in the vertical and 12. Hausding, Jan, Lorenz, Enrico, Oretlepp, Regine, Lundahl, Anna. horizontal directions the design area for the required warp Application of stitch-bonded multi-plies made by using the extended warp knitting process: reinforcements with symmetrical layer knitted structures. arrangement for concrete. Journal of the Textile Institute, 2011, p. 1. 13. E.h. Glaessgen1, I.S. Raju2 and C.C. Poe, Jr.2 modeling the influence 5.5. Applications of stitching on delamination growth in stitched warp-knit composite The formulated equation is applicable to warp knitted lap joints, 1National Research Council, 2Mechanics of Materials Branch NASA Langley Research Center, Hampton, VA, 23681 structures such as crochet with its derivatives, tricot with its 14. Dow, M.B. and Dexter, H.B., “Development of Stitched, Braided derivatives, atlas with its derivatives and other structures with and Woven Composite Structures in the ACT Program and at up to two needle bars and more guide bars. But it has Langley Research Center,” NASA TP-97-206234, November 1997 limitations for structures such as double rib tricot fabrics. 15. Marzieh Javadi Toghchi and Saeed Ajeli, Investigation into the Geometrical Loop Effect on Tensile Behavior of Single Bar Warp- Knitted Fabric Using Finite Element Method, JOURNAL OF 6. CONCLUSION TEXTILES AND POLYMERS, VOL. 1, NO. 1, JANUARY 2013. 16. H. Dabiryan and A. A. A. Jeddi, “Analysis of warp knitted fabric Textile industries are vital for serving one of human being structure. Part II: theoretical study on initial modulus of warp knitted fabrics (tricot, locknit, and satin)”, J. Text. I., vol.103, no. 9, need called clothing especially for developing countries. pp. 997–1011, 2012. These countries use more of hand operated, mechanical 17. O. Goktepe and S. C.Harlock, “A three-dimensional loop model for machines and manual designing tools and materials. In visual simulation of warp-knitted structure”, J. Text. I., vol. 93, developing countries using designing software is not no.1, pp. 11-28, 2002. common since it is expensive and not available easily. Rather we use pen, pencil, paper and little extent computer Microsoft excel and word. With these material if designers made mistake they drop the wrong material or try to erase which will reduces the quality and neatness. For these and other reasons this developed formula is provided. With further research, hopefully the limitations of this formula will be eliminated and well defined formula for all types of warp knitted structures can be developed. Finally I would like to thank my students those helping me by practicing this equation in different structures for the success of this work.

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